This week M&S announced that its like-for-like food sales had fallen by 3% in the 13 weeks to April 2.
Acting director of food Guy Farrant has been in the role since June last year, and is still believed to be one of the frontrunners for the job.
Chief executive Stuart Rose said that sales at the 129 Simply Food stores and its out of town outlets were strong, while the stores with the most problems were its city-centre sites.
In a bid to arrest the decline, M&S is extending its trial of new-format stores with deli-style food halls into Birmingham, the first in a major city-centre store.
Work began on the store this week and is due to be completed in the autumn. It will bring the total of converted stores to six, while all new store openings this year will also carry the deli format.
Despite the poor sales results, shares in M&S rallied this week, with many city analysts believing it had turned the corner.
In the past year, M&S has asked for reductions on its suppliers invoice costs, and the impact of these has yet to be felt in the company’s results.